El efecto de arco aplicado a sistemas de bloques
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Aguirre Izaquita, Daniel Arnulfo
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Resumen. Se analizan dos sistemas que presentan el efecto de arco: arco de cilindros y arco de poliedros rectangulares. El objetivo es calcular las fuerzas interparticulares y otras variables de respuesta como ángulos de fricción interna, momentos, etc. Se definen métodos programables para cada caso y se analiza la falla. En el arco de esferas se plantean y resuelven las ecuaciones de equilibrio de cada partícula secuencialmente. De tal manera que se obtienen las resultantes entre fuerzas normales y cortantes friccionales, denominadas empujes, los ángulos de fricción y los momentos en cada partícula; luego se usa un método de prueba y error para calcular la deformada del sistema. En general se obtiene que el sistema no tiende a ser estable según lo obtenido para las condiciones deformadas del sistema. Se obtienen mejoras del comportamiento al añadir cohesión al sistema. Para el arco con bloques o viga tajada, la metodología, basada en la elasticidad, calcula el valor de flecha máxima que genera fuerzas interparticulares, producto de los traslapos entre bloques, que equilibran el momento generado por las fuerzas externas al sistema. Luego se aplica la metodología de equilibrio límite determinando los modos de falla respectivos. Se ejecuta el método de relajación de Brady-Brown, cuyos resultados se comparan contra la tesis para confirmar la concepción empírica de que cuanto más discontinuidades tenga un sistema, su comportamiento será menos competente, debido a que con el método de tesis, la respuesta del sistema es más cercana a la falla. Se establece el modo de falla denominado “Capacidad máxima debida al momento interno”.
Abstract:Two systems showing the arching effect are analyzed; cylinders arch and rectangular polyhedron arch. The objective is to estimate interparticular forces and the other variables of response as friction angles, moments, etc. Programmable methods are defined for each case and failure is analyzed. In the spheres arch, equilibrium equations of each particle are stated and solved sequentially. In this way, resultants between normal and shear forces are obtained and named “Empuje”, also friction angles and moments in each particle are also estimated; then a trial and error method is used to estimate the deformed condition of the system. In general, it is observed that the system is not stable according to the deformed results. After adding cohesion at the system, an improvement in the behavior is observed. Analyzing the blocks arch or voussoir beam, the methodology, based in elasticity, estimates the value of maximum deflection that generates the interparticular forces, produced by overlaps between blocks, that equilibrates the moment generated by external forces to the system. Then, limit equilibrium methodology is applied to define the respective failure modes. The Brady-Brown’s relaxation method is executed, which results are against the thesis confirming the empirical statement that suggest that the more discontinuities has a rock massif, the less competent will be its behavior, due that the thesis ethos reveals results closer to the failure. Also, the failure mode called “Maximum capacity due to the intern moment” is explained and stated.
Abstract:Two systems showing the arching effect are analyzed; cylinders arch and rectangular polyhedron arch. The objective is to estimate interparticular forces and the other variables of response as friction angles, moments, etc. Programmable methods are defined for each case and failure is analyzed. In the spheres arch, equilibrium equations of each particle are stated and solved sequentially. In this way, resultants between normal and shear forces are obtained and named “Empuje”, also friction angles and moments in each particle are also estimated; then a trial and error method is used to estimate the deformed condition of the system. In general, it is observed that the system is not stable according to the deformed results. After adding cohesion at the system, an improvement in the behavior is observed. Analyzing the blocks arch or voussoir beam, the methodology, based in elasticity, estimates the value of maximum deflection that generates the interparticular forces, produced by overlaps between blocks, that equilibrates the moment generated by external forces to the system. Then, limit equilibrium methodology is applied to define the respective failure modes. The Brady-Brown’s relaxation method is executed, which results are against the thesis confirming the empirical statement that suggest that the more discontinuities has a rock massif, the less competent will be its behavior, due that the thesis ethos reveals results closer to the failure. Also, the failure mode called “Maximum capacity due to the intern moment” is explained and stated.